In these webpages we start by trying to visualise the desired locus and to describe its shape in a qualitative way.

We then construct the locus, ie derive it empirically. The result might surprise you or your students.

We then consider what happens to the locus when we vary the multiplier connecting AP and BP, and finally we move towards a proof about the nature of the locus's shape.

a high-res pdf file of this new GEOaa-zz task